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A hypergraph Turán problem with no stability
release_c2dqczlaoffgdj52cgvsih23iu
by
Xizhi Liu, Dhruv Mubayi
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as a article
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2019
Abstract
A fundamental barrier in extremal hypergraph theory is the presence of many
near-extremal constructions with very different structure. Indeed, the
notorious Turán problem for the complete triple system on four points most
likely exhibits this phenomenon. We construct a finite family of triple systems
M, determine its Turán number, and prove that there are two
near-extremal M-free constructions that are far from each other in
edit-distance. This is the first extremal result for a hypergraph family that
fails to have a corresponding stability theorem.
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1911.07969v1
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